Question

Two opposite sides of a parallelogram each have a length of `9`. If one corner of the parallelogram has an angle of `(7 pi)/8` and the parallelogram's area is `54`, how long are the other two sides?

Answer 1

Length of other pair of sides is `15.678`

Explanation:

Area of a parallelogram is given by `axxbxxsintheta`, where `a` is length of one pair of equal sides and `b` is the length of other pair of sides of a parallelogram and `theta` is the angle between them.

As area of the parallelogram is `54`, one pair of sides is `9` and included angle is `sin(7pi/8)`

`54=9xxbxxsin(7pi/8)`

or `54=9xxbxx0.3827`

or `b=54/(9xx0.3827)=54/3.4443=15.678`

Hence, length of other pair of sides is `15.678`